In unconfirmed reports, the man was stabbed on the High Street in the town. The High Street has now been cordoned off. The victim’s condition is not yet known. His identity and age also remain unknown.
It has not been confirmed if the assailant has been arrested or remains at large.
Kent 999, an account which reports on emergency service incidents, reported the alleged attack.
They said: “Part of the High Street cordoned off for an investigation following an unconfirmed report of one man being stabbed in the neck by another man near Iceland.
The alleged attack came after police launched an investigation into the death of a man in his 60s.
Officers were called to the disturbance at 5.21pm on Thursday in Lullingstone castle in Eynsford.
The man was pronounced dead shortly afterwards.
A Kent police spokesman said officers had been told “rocks were being thrown”.
They added that it was believed the man had been in an altercation with two boys or teenagers.
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Police have insisted the attack was an isolated case.
Writing to local Tory MP Laura Trott on her Facebook page, Stephen Jury said: “Something needs to be done. The level of anti-social behaviour in and around the villages has become a joke.
“There have been several instances over the last week or so… I just feel for that poor man’s family but something like this was coming.”
Kent Police later released a statement confirming they had been called to the scene at 5.21pm to a disturbance.
A statement added: “A man later died at the scene and officers from the Kent and Essex Serious Crime Directorate are investigating.
“It was reported that rocks were being thrown.”
A crime scene was still in place on Friday morning.
Police have also appealed for any information of the attacks or from anybody who was in the area including anglers, golfers or dog walkers.